关于随机环境中磁场诱导的随机运动
On the Stochastic Motion Induced by Magnetic Fields in Random Environments.
作者信息
Kang Yun Jeong, Jung Jae Won, Seo Sung Kyu, Kim Kyungsik
机构信息
School of Liberal Studies, Wonkwang University, Iksan 54538, Republic of Korea.
DigiQuay Company Ltd., Seoul 06552, Republic of Korea.
出版信息
Entropy (Basel). 2025 Mar 21;27(4):330. doi: 10.3390/e27040330.
Here, we study the Navier-Stokes equation for the motion of a passive particle based on the Fokker-Planck equation in an incompressible conducting fluid induced by a magnetic field subject to an exponentially correlated Gaussian force in three-time domains. For the hydro-magnetic case of velocity and the time-dependent magnetic field, the mean squared velocity for the joint probability density of velocity and the magnetic field has a super-diffusive form that scales as ∼t3 in t>>τ, while the mean squared displacement for the joint probability density of velocity and the magnetic field reduces to time ∼t4 in t<<τ. The motion of a passive particle for τ=0 and t>>τ behaves as a normal diffusion with the mean squared magnetic field being <h2(t)>∼t. In a short-time domain t<<τ, the moment in the magnetic field of the incompressible conducting fluid undergoes super-diffusion with μ2,0,2h∼t6, in agreement with our research outcome. Particularly, the combined entropy H(v,h,t) (H(h,v,t)) for an active particle with the perturbative force has a minimum value of ∼lnt2 (∼lnt2) in t>>τ (τ=0), while the largest displacement entropy value is proportional to lnt4 in t<<τ and τ=0.
在此，我们基于福克 - 普朗克方程研究在由磁场诱导的不可压缩导电流体中，在三个时域内受指数相关高斯力作用的被动粒子运动的纳维 - 斯托克斯方程。对于速度和随时间变化的磁场的磁流体情况，速度与磁场联合概率密度的均方速度具有超扩散形式，在(t>>\tau)时按(\sim t^3)缩放，而速度与磁场联合概率密度的均方位移在(t<<\tau)时减小到(\sim t^4)。对于(\tau = 0)且(t>>\tau)，被动粒子的运动表现为正常扩散，均方磁场为(<h^2(t)>\sim t)。在短时间域(t<<\tau)中，不可压缩导电流体磁场中的矩经历超扩散，(\mu_{2,0,2h}\sim t^6)，这与我们的研究结果一致。特别地，对于具有微扰力的主动粒子，组合熵(H(v,h,t))（(H(h,v,t))）在(t>>\tau)（(\tau = 0)）时具有最小值(\sim \ln t^2)（(\sim \ln t^2)），而在(t<<\tau)且(\tau = 0)时最大位移熵值与(\ln t^4)成正比。
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